Question

Philip is sorting acorns he collected. He has 92 acorns: 66 still have their tops, 26 do not. Philip wants to sort the acorns into groups with the same number of acorns, including some with and without tops. He wants each group to have an equal number of acorns with tops and an equal number of acorns without tops. Which answer best shows how Philip can represent how he should sort the acorns?(1 point)
Responses

2(33+13)
2 left parenthesis 33 plus 13 right parenthesis

6(11+4)
6 left parenthesis 11 plus 4 right parenthesis

1(66+26)
1 left parenthesis 66 plus 26 right parenthesis

24(3+1)
24 left parenthesis 3 plus 1 right parenthesis
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Answer 1

To determine how Philip can sort the acorns in equal groups with the same number of tops and bottoms, we need to look for a factorization that splits the total of 92 acorns evenly into groups, while balancing the number of acorns with and without tops.

Philip has:
- 66 acorns with tops
- 26 acorns without tops

To satisfy his requirement of equal grouping, we can use the greatest common divisor (GCD) or other factors of the total acorns to create groups.

Let's check the options:

1. **2(33 + 13)**:
- This represents 2 groups with 33 acorns with tops and 13 acorns without tops in each group.
- Checking: 2 groups mean \(2 \times 33 = 66\) with tops and \(2 \times 13 = 26\) without tops, which is correct.

2. **6(11 + 4)**:
- This represents 6 groups with 11 acorns with tops and 4 acorns without tops in each group.
- Checking: 6 groups mean \(6 \times 11 = 66\) with tops and \(6 \times 4 = 24\) without tops, given that 24 is not adequate since he has 26 without tops.

3. **1(66 + 26)**:
- This represents 1 group with all acorns. This does not fit the requirement of sorting into groups.

4. **24(3 + 1)**:
- This represents 24 groups with 3 tops and 1 without in each group.
- However, checking shows \(24 \times 3 = 72\) with tops, which exceeds the number he has.

The best representation of how Philip can sort the acorns into equal groups, maintaining the balance of acorns with and without tops, is **2(33 + 13)**.

Final answer: **2(33+13)**